BEIRUT—The Syrian regime regained control of the ancient city of Palmyra on Sunday, its first significant victory over Islamic State and the latest in a string of territorial losses for the extremist group.

Capturing Palmyra could open a gateway to militant strongholds to the northeast, in the provinces of Raqqa and Deir Ezzour, though there are no signs Syria and its allies are prepared to launch a broader offensive soon.